Although you can put your mind to rest regarding collateral damage from the timing belt situation, you have to consider what other vital maintenance procedures the former owner decided to NOT do.
Unless you can confirm that the transmission fluid was changed every 30k, you need to change the trans fluid and filter a.s.a.p. Although you dodged a bullet with the timing belt, a 6 year old car that has had no transmission maintenance is a candidate for early transmission failure.
For this service, take the car to an independent transmission shop that has been in business for at least 3 years. DO NOT take the car to AAMCO, Lee Myles, Mr. Transmission, Cottman, or any other chain operation unless you want to be told that you need a rebuilt transmission–and to be overcharged for that unnecessary transmission rebuilding.
After the transmission has been serviced, then you and your regular mechanic can assess whether the car needs new spark plugs, air filter, fuel filter, spark plug wires, a coolant change, and a brake fluid change. In the absence of maintenance records, you have to assume that these procedures have never been done.